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Quaestiones Mathematicae 2005, 28 (1) : 123–135
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The m-convergence theory in fuzzy topological spaces
Authors:
Q Li
Department of Applied Mathematics, Hunan University, Changsha 410082, Hunan, China
Corresponding Author: Q Li (E-mail: liqingguoli@yahoo.com.cn)
Abstract:
In this paper, the m-convergences of fuzzy nets and fuzzy filters are introduced in a fuzzy topological space. The relations between m-convergences of fuzzy nets and fuzzy filters are investigated as are the relations between Hausdorff fuzzy topology and m-convergences of fuzzy nets and fuzzy filters. Characterizations of Hausdorff fuzzy topology in terms of neighborhoods and quasi-coincident neighborhoods and of minimal Hausdorff fuzzy topology in terms of m-convergence of fuzzy filters, are established. We study the relations between m-convergence of fuzzy nets and m-compactness, and between minimal Hausdorff fuzzy topology and m-compactness in a fuzzy topological space.
Mathematics Subject Classification (2000): 54A40.
Keywords: Fuzzy net; fuzzy filter; m-convergence; m-compactness; minimal Hausdorff
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